Question: Simplify the following expression: $\sqrt{3}+\sqrt{12}+\sqrt{48}$
Solution: First, try to factor any perfect squares out of the radicals. $= \sqrt{3}+\sqrt{12}+\sqrt{48}$ $= \sqrt{3}+\sqrt{4 \cdot 3}+\sqrt{16 \cdot 3}$ Separate the radicals and simplify. $= \sqrt{3}+\sqrt{4} \cdot \sqrt{3}+\sqrt{16} \cdot \sqrt{3}$ $= \sqrt{3}+2\sqrt{3}+4\sqrt{3}$ Finally, simplify by combining the terms. $= ( 1 + 2 + 4 )\sqrt{3} = 7\sqrt{3}$